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A parallel plate capacitor has plates of...

A parallel plate capacitor has plates of area A separated by distance ‘d’ between them. It is filled with a dielectric which has a dielectric constant that varies as `k(x)=K(1+ax)` where ‘x’ is shown in figure. If `(al)lt lt 1` , the total capacitance of the system is best given by the expression:

A

`(A in_(0)K_(0))/(d) (1 + (alpha^(2) l^(2))/(2))`

B

`(A in_(0)K_(0))/(d) (1 + alpha l)`

C

`(A in_(0)K_(0))/(d) (1 + (2l^(2))/(4))`

D

`(A in_(0)K_(0))/(d) (1 + (alpha l)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
All dC.s are in parallel
A= bl

`C= int dC, dC= (in_(0)bdyK)/(d)`
`therefore C= (in_(0)bK_(0))/(d) underset(0)overset(l)int (1 + alpha y)dy= (in_(0)b K_(0)l)/(d) (1 + (alpha l)/(2))`
`C= (A in_(0)K_(0))/(d) (1 + (alpha l)/(2))`
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